Stability and periodicity in coupled Pinney equations
type: Item
instance of: scholarly article
title: Stability and periodicity in coupled Pinney equations
zbMATH Open document ID: 0765.34032
DOI: 10.1016/0022-0396(92)90126-8
author: S. Singh
published in: Journal of Differential Equations
publication date: 1993-01-17T00:00:00Z
review text: The author studies the correspondence (established in an earlier paper) between solutions of the coupled Pinney equations \(d^ 2x/dt^ 2+\omega^ 2(t)x=-\alpha xy^{-4}+\beta x^{-3}\), \(d^ 2y/dt^ 2+\omega^ 2(t)y=-\gamma yx^{-4}+\delta y^{-3}\) and the associated Hill's equations. It is shown that stability (periodicity) of the general solution of the linearized system (Hill's equations) is sufficient for stability (periodicity) of solutions to the original nonlinear system.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 97340
zbMATH Keywords: periodic solutions
zbMATH Keywords: coupled Pinney equations
zbMATH Keywords: Hill's equations
zbMATH Keywords: stability
zbMATH Keywords: linearized system
zbMATH Keywords: nonlinear system
reviewed by: Marian Mrozek
MaRDI profile type: Publication
full work available at URL: 0022-0396(92)90126-8
OpenAlex ID: W2089928456
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description: scientific article; zbMATH DE number 97340